Modified FrontEnd to parse & highlight function definitions for compilability?

Question

I suspect this would require advanced MMA skills, but it would be very useful if one could modify the front end so that any MMA defined function calls in a Compile[] could be flagged if they are not compilable, because uncompilable functions would cause slow compiled code through calls to MainEvaluate[].

Question 1096 shows how to get lists of compilable functions.

How might the functions in a Compile[] definition be dynamically checked against such a list (i.e. as the user types them) and highlighted in some way if they are/are not compilable?

(I have not yet got around to calling a compiled function from a compiled function, but the obvious next step would be to maintain a secondary list of user defined functions that can be called in a Compile[] and to provide similar highlighting.

Would someone exceedingly smart be able to see how to do both these things?)

UPDATE/Amendment

It has been pointed out in comments and through a linked question, whose significant content I have quoted, that "compilable?" is not a simple question to answer. I would therefore like to amend the question as follows:

How could one customize the front-end (so that feedback is immediate on typing) so that MMA defined functions that are not listed as compilable (whether conditionally or not) are highlighted if used inside a Compile[]?

Rationale: one cannot easily say a function is compilable, but given that there are lists of MMA functions that may be compilable, any function not on that list may be assumed non-compilable and the sooner one can see that the less effort one is likely to waste writing a function for compilation that, ultimately, cannot compile. [The other suggestions may then be incorporated to ease the process of determining whether compilation then actually succeeded without calls to MainEvaluate]

Answer 1

One idea is to use the AutoStyleWords option of cells to color selected words. For example, the following stylesheet colors all words given by Compile`CompilerFunctions the color RGBColor[.3, .5, .5] indicating that they are acceptable compiler functions, and other words will remain black, indicating that they are probably not compiler functions:

SetOptions[
    EvaluationNotebook[],
    StyleDefinitions -> Notebook[
        {
        Cell[StyleData[StyleDefinitions->"Default.nb"]],
        Cell[StyleData["CompileInput", StyleDefinitions->StyleData["Input"]],
            AutoStyleWords->(SymbolName[#]->"CompiledFunction"&/@Compile`CompilerFunctions[])
        ]
        ,
        Cell[StyleData["CompiledFunction"], FontColor->RGBColor[.3,.5,.5]]
        },
        StyleDefinitions->"PrivateStylesheetFormatting.nb"
    ]
]

Then, here's an example of a compiled function using the "CompileInput" style:

You can see that IntegerQ and MatchQ have been flagged as noncompilable functions.

Answer 2

Okay so this is not an answer (it's to big to write a comment for) to your exact question but a dirty workaround. But it works.

We can write a simple wrapper for Compile which warns us if we get MainEvaluates and Prints them.

Attributes[CompileEx]={HoldAll};
CompileEx[a___]:=Module[{cf,printString,meCases},
cf=Compile[a];
Needs["CompiledFunctionTools`"];
printString=CompiledFunctionTools`CompilePrint[cf];
meCases=StringCases[printString,"MainEvaluate["~~pattern:Repeated[Except["\n"]]~~"]":>pattern];
If[Length[meCases]>0,Print[ToString[Length[meCases]]<>" MainEvaluates detected.\n\n"<>StringJoin[Riffle[meCases,"\n\n"]]]];
cf
]

This does only printing but its easy to let it throw an error or something you would prefer.

A Testrun:

CompileEx[{{i}},If[MatchQ[i,_?OddQ],If[MatchQ[i,_?IntegerQ],Sin[i]^2,0],0]]

2 MainEvaluates detected.

Function[{i}, MatchQ[i, _?OddQ]][ R0]

Function[{i}, MatchQ[i, _?IntegerQ]][ R0]

CompiledFunction[...]

You can save the definition of CompileEx to a package and load it or save it in the kernel/init.m to have it always by you.

I know its not the best solution but hey, better than nothing. But i'm sure, someone here is able to tweek the FrontEnd to do what you want.